Consider the following sets of quantum numbers: \(\begin{array}{|c|c|c|c|c|} \hline & n & l & m & s \\…
Consider the following sets of quantum numbers:
\(\begin{array}{|c|c|c|c|c|} \hline & n & l & m & s \\ \hline \text {(i) } & 3 & 0 & 0 & +1 / 2 \\ \text {(ii) } & 2 & 2 & 1 & +1 / 2 \\ \text {(iii) } & 4 & 2 & -2 & -1 / 2 \\ \text {(iv) } & 1 & 0 & -3 & -1 / 2 \\ \text {(v) } & 3 & 2 & 3 & +1 / 2 \\ \hline \end{array}\)
Which of the following sets of quantum number is not possible?
(i), (ii), (iii) and (iv)
(ii), (iv), and (v)
(i), and (iii)
(ii), (iii) and (iv)
Solution
(ii) is not possible for any value of $n$ because $l$ varies from 0 to $(n-1)$ thus for $n=2$, can be only $0,1,2$.
(iv) is not possible because for $l=0$, $m=0$.
(v) is not possible because for $l=2$, $m$ varies from -2 to +2 .
Related Theory
The value of the spin quantum number is independent of principal, azimuthal and magnetic quantum number. It is never possible that two electrons in the same orbital will have the value of all four quantum numbers the same.